1844: Card Trick

The magician shuffles a small pack of cards, holds it face down and performs the following procedure:

• The top card is moved to the bottom of the pack. The new top card is dealt face up onto the table. It is the Ace of Spades.
• Two cards are moved one at a time from the top to the bottom. The next card is dealt face up onto the table. It is the Two of Spades.
• Three cards are moved one at a time…
• This goes on until the nth and last card turns out to be the n of Spades.

This impressive trick works if the magician knows how to arrange the cards beforehand (and knows how to give a false shuffle). Your program has to determine the initial order of the cards for a given number of cards, 1 ≤ n ≤ 13.

On the first line of the input is a single positive integer, telling the number of test cases to follow. Each case consists of one line containing the integer n.

For each test case, output a line with the correct permutation of the values 1 to n, space separated. The first number showing the top card of the pack, etc…

2
4
5

2 1 4 3
3 1 4 5 2